Heisenberg Antiferromagnet on a 1/7-Depleted Triangular Lattice

Based on the triangular lattice and its depletions there are three simple frustrated antiferromagnetic Heisenberg models in two dimensions. The first two, the triangular and kagomé lattices, have been examined in the recent past. The triangular lattice seems to have a long range order whereas the kagomé does not show the long range order. But these results are still controversial. This work is concentrated on a third type of this lattice family in order to improve the understanding of the connection between the long range order and coordination number in low dimensional systems. Bets has described the geometric properties of this lattice. It has a coordination number 5, which lies precisely between coordination numbers 6 and 4 of the other two lattices. The low-lying spectra and the correlation functions of finite lattices have been examined to discuss the possibility of a long range ordered ground state in the 1/7-depleted triangular lattice. The low-lying spectrum is generated by an exact diagonalization, and the tower of states behavior points to a long range ordered ground state.